35775 ÷ 4 = 8943 R3
Let's divide 35775 by 4.

Step 1:
4 goes into 3 0 times with a remainder of 3.
Write down 0 as next digit of of the result. 
Result so far: 0
Subtract 0 from 3 to get 3.
Bring next digit (5) of the dividend behind the 3 and repeat the process: 35 / 4

Step 2:
4 goes into 35 8 times with a remainder of 3.
Write down 8 as next digit of of the result. 
Result so far: 8
Subtract 32 from 35 to get 3.
Bring next digit (7) of the dividend behind the 3 and repeat the process: 37 / 4

Step 3:
4 goes into 37 9 times with a remainder of 1.
Write down 9 as next digit of of the result. 
Result so far: 89
Subtract 36 from 37 to get 1.
Bring next digit (7) of the dividend behind the 1 and repeat the process: 17 / 4

Step 4:
4 goes into 17 4 times with a remainder of 1.
Write down 4 as next digit of of the result. 
Result so far: 894
Subtract 16 from 17 to get 1.
Bring next digit (5) of the dividend behind the 1 and repeat the process: 15 / 4

Step 5:
4 goes into 15 3 times with a remainder of 3.
Write down 3 as next digit of of the result. 
Result so far: 8943
Subtract 12 from 15 to get 3.

The final result is 8943 with a remainder of 3.